Theory of Machine
A rigid body, under the action of external forces, can be replaced by two masses placed at a fixed distance apart. The two masses form an equivalent dynamical system, if

All of these
The sum of mass moment of inertia of the masses about their center of gravity is equal to the mass moment of inertia of the body
The sum of the two masses is equal to the total mass of body
The center of gravity of the two masses coincides with that of the body

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Theory of Machine
Hammer blow

Is the maximum vertical unbalanced force caused by the mass added to balance the reciprocating masses
Varies as the square root of the speed
Is the maximum horizontal unbalanced force caused by the mass provided to balance the reciprocating masses.
Varies inversely with the square of the speed

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Theory of Machine
The secondary unbalanced force due to inertia of reciprocating parts in a reciprocating engine is given by (where m = Mass of reciprocating parts, ω = Angular speed of crank, r = Radius of crank, θ = Angle of inclination of crank with the line of stroke, and n = Ratio of the length of connecting rod to radius of crank)

m.ω².r sinθ
m.ω².r (cos 2θ/n)
m.ω².r cosθ
m.ω².r (sin 2θ/n)

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